An experimental analysis of Global Positioning System (GPS) flight data collected onboard a Small Unmanned Aerial Vehicle(SUAV) is conducted in order to demonstrate that postprocessed kinematic Precise Point Positioning (PPP) solutions withprecisions approximately 6 cm 3D Residual Sum of Squares (RSOS) can be obtained on SUAVs that have short duration flightswith limited observational periods (i.e., only ∼≤5 minutes of data). This is a significant result for the UAV flight testing communitybecause an important and relevant benefit of the PPP technique over traditional Differential GPS (DGPS) techniques, such asReal-Time Kinematic (RTK), is that there is no requirement for maintaining a short baseline separation to a differential GNSSreference station. Because SUAVs are an attractive platform for applications such as aerial surveying, precision agriculture, andremote sensing, this paper offers an experimental evaluation of kinematic PPP estimation strategies using SUAV platform data.In particular, an analysis is presented in which the position solutions that are obtained from postprocessing recorded UAV flightdata with various PPP software and strategies are compared to solutions that were obtained using traditional double-differencedambiguity fixed carrier-phase Differential GPS (CP-DGPS). This offers valuable insight to assist designers of SUAV navigationsystems whose applications require precise positioning.
1. Introduction
The Precise Point Positioning (PPP) technique was intro-duced in the late nineties [1, 2] and uses state-space GNSSsatellite orbit and clock bias solutions with significantlygreater accuracy than their broadcast ephemeris counterpartsin order to enable the user-segment to obtain accuratepositioningwith undifferenced data.Theuse of undifferenceddata means that no GNSS reference station is required toform differential data combinations. To date, PPP technologyhas matured to the extent that there are now multiple real-time orbit and clock solution products offered by govern-ment organizations [3], commercial entities [4, 5], and theInternational GNSS Service [6]. The PPP technique hasrevolutionized many geophysical research applications thatinvolve static reference stations and Earth orbiting spacecraft;however, it has not been heavily exploited for applicationsinvolving low-cost small UAVs (SUAVs).
Many authors have conducted studies to compare thesolution accuracy of the PPP technique with double-difference CP-DGPS solutions or other ground “truths.” For
example, Colombo et al. show that once a PPP filter hasconverged, it agrees with double-differenced GPS to within10 cm [7]. Likewise, for a kinematic vehicular application,Honda et al. demonstrate a few decimeter-level performancewith respect to CP-DGPS [8]. In another study, Zhang andForsberg consider the use of PPP to support missions thatrequire accuracy over very long-ranges (i.e., on the orderof many hundreds of kilometers), thereby making double-differences to an individual reference station impractical [9].In their assessment, Zhang and Forsberg use comparisonsof airborne laser altimetry and satellite altimetry productsto assess height solution accuracy from PPP and concludethat PPP can produce accuracy at the decimeter-level. In2009, Bisnath andGao [10] offered insight on the state-of-the-art of PPP and, in their assessment, demonstrate decimeter-level kinematic PPP of a static reference station after aninitial convergence period. Bisnath and Gao conclude thatmore algorithm development and additional observables areneeded to reduce PPP’s convergence period before it can beconsidered as an RTK alternative. Many have shown that PPP
Hindawi Publishing CorporationInternational Journal of Aerospace EngineeringVolume 2016, Article ID 1259893, 11 pageshttp://dx.doi.org/10.1155/2016/1259893
2 International Journal of Aerospace Engineering
can achieve accuracy levels consistent with CP-DGPS butpoint out its slow convergence.
More recent studies have also considered the impact ofmulticonstellation GNSS or other navigation systems, suchas Inertial Navigation Systems (INS), to yield better accuracywith the PPP approach. For example, Cai et al. evaluatedmulticonstellation GNSS using the GPS, GLONASS, Galileo,and Beidou and showed improvements in kinematic PPPposition solution accuracy and convergence [11]. Likewise,Yigit et al. demonstrated better positioning performancewith multiconstellation GNSS, especially whenever there isa relatively short observation duration [12]. In addition,Zhang and Gao include INS within a PPP filter for akinematic application and show faster solution convergenceand accuracy comparable to conventional RTK/INS solutions[13]. More recently, Gross et al. [14] reaffirmed better overallsolution accuracy as well as solution robustness to rapidchanges in the tropospheric delay induced by abrupt changesin aircraft altitude by comparing both a fused PPP/INS and aPPP-only solution to a postprocessed reference solution thatwas the NASA Jet Propulsion Laboratory’s submission to theUS National Geodetic Survey’s Kinematic GPS ProcessingChallenge [15]. Finally, Watson et al. [16] provided a compre-hensive evaluation of the benefit of incorporating INS undervarious common PPP error sources by using a Monte Carlosimulation environment and showed that incorporating INSbecomes more important depending on the quality of thetroposphere model, multipath environment, and quality ofPPP orbit and clock products.
Despite the extensive literature that offers performancecomparisons of different GNSS processing techniques, thereis a lack of published studies that demonstrate the obtainablePPP positioning accuracy of SUAV flights that have verylimited flight durations. Furthermore, while several paststudies point to the slow solution convergence as a pitfallof using PPP technique, the need for real-time solutions isoften irrelevant for many SUAV scientific applications (e.g.,remote sensing, aerial mapping) that can simply wait forpostprocessed solutions. However, because some SUAVs havevery limited flight durations, which are on the order offifteen minutes, or often less, some uncertainty remains asto whether PPP’s slow solution convergence will impact theaccuracy of the postprocessed (i.e., filtered and backwardssmoothed) short duration SUAV solutions.
As such, to fill this knowledge gap, the contribution of thispaper is to offer an experimental analysis of PPP techniqueswhen compared to CP-DGPS with data collected onboardSUAV that has very short duration flights.This is particularlyrelevant to the field robotics community as SUAVs arebeing more regularly used for more ambitious scientificapplications that have stringent requirements on platformpositioning. For example, recent experimental evaluationshave demonstrated the use of Light Detection and Ranging(LIDAR) for fine-scale mapping with UAVs [17–19]. Accurategeoregistration requires platform positioning accuracy in thecm-scale, as these LIDAR systems have cm-scale or better res-olution. Additionally, researchers at the University of Kansashave recently instrumented SUAV for radar sounding ofremotely located Antarctic ice sheets [20]. While the current
Kansas ice sounding UAV is operating at radar frequencieswith large wavelengths, it is not a stretch to envision asimilar SUAV radar systemoperating higher frequencies (e.g.,microwave) and thus needing cm-scale positioning precision,such as a miniaturized version of NASA’s L-Band UAVSARinstrument [21]. For these SUAV applications, which aretypically cited to offer the benefit of being rapidly deployableand useful for remote regions, eliminating the need for GNSSdifferential reference station and thus reducing overall costand complexity of the navigation system by leveraging PPPwill further open the use of SUAVs for hosting scientificpayloads that have stringent positioning requirements.
The rest of this paper is organized as follows. Section 2reviews the GNSS observational models for both PPP, whichis being evaluated, and double-differenced ambiguity fixedCP-DGPS, which is being used to estimate reference positionsolutions. In addition, the details of the software implementa-tion employed in this study are discussed. Section 3 discussesthe experimental SUAV, GNSS equipment, and flight-testenvironment used for this study.The results of an experimen-tal comparison study are then detailed in Section 4, and thestudy’s findings are summarized in Section 5.
2. Methodology
2.1. Observational Models. We start by considering thegeneric observation models for GNSS pseudorange andcarrier-phase measurements as shown in (1) and (2), whichare found in many textbooks [22, 23]. Consider
𝜌
𝑗
𝑖 = 𝑅
𝑗
𝑖 + 𝑐𝛿𝑡𝑖 + 𝑇
𝑗
𝑖 + 𝐼
𝑗
𝑖 + 𝑐𝛿𝑡
𝑗+ 𝜖
𝑗𝜌, (1)
Φ
𝑗
𝑖 = 𝑅
𝑗
𝑖 + 𝑐𝛿𝑡𝑖 + 𝑇
𝑗
𝑖 − 𝐼
𝑗
𝑖 + 𝑐𝛿𝑡
𝑗+ 𝜆𝐿𝑘
𝑁
𝑗
𝐿𝑘+ 𝜖
𝑗
Φ. (2)
In (1) and (2), the subscript 𝑖 is used to denote the user andsuperscript 𝑗 denotes the GNSS satellite index. Common toboth pseudorange and carrier-phase are several error sources,where 𝑡𝑖 is the unknown GNSS receiver clock bias in unitsof seconds, 𝑡𝑗 is the GNSS transmitter’s clock bias in unitsof seconds, 𝑐 is the speed of light in a vacuum in units ofmeters per second, 𝑇𝑗𝑖 is the GNSS signal delay due to therefraction in the neutral atmosphere in units of meters, and𝐼
𝑗
𝑖 is the phase-advance/pseudorange delay caused by signalrefraction through traversing the Earth’s ionosphere (notethe sign change between (1) and (2)) in units of meters. Theremaining unmodeled error sources are denoted by 𝜖 andare in units of meters. Within the carrier-phase model (2),there is also unknown integer phase tracking ambiguity that isdenoted by𝑁𝑗𝑖 and is taken from units of carrier-phase cyclesto meters through a multiplication with the GNSS carrierwavelength 𝜆𝐿𝑘
, where 𝑘 = 1, 2 and 𝐿1 = 19.0 cm and 𝐿2 ≈
24.4 cm for the case of GPS. Furthermore, in (1) and (2), thegeometric range between the user’s receiver antenna phasecenter and the satellite’s transmitter antenna phase center isdenoted as 𝑅𝑗𝑖 and given by
𝑅
𝑗
𝑖 =√
(𝑥
𝑗− 𝑥𝑖)2+ (𝑦
𝑗− 𝑦𝑖)2+ (𝑧
𝑗− 𝑧𝑖)2,
(3)
International Journal of Aerospace Engineering 3
where both the user’s position and satellite’s position aremodeled in the same Cartesian reference frame, typicallyeither an Earth-Centered-Earth-Fixed frame or an Earth-Centered-Inertial frame. For the PPP technique, accuratesolutions to eachGNSS transmitter’s clock bias, 𝑡𝑗, and orbitallocation (𝑥
𝑗, 𝑦
𝑗, 𝑧
𝑗) are determined using a global network
of tracking reference stations and are used in lieu of theGNSS broadcast ephemeris. However, typically, the satellitelocations are provided with respect to the center of gravity ofeachGNSS spacecraft.Therefore, to be consistentwith (3), theattitude of each satellite must be modeled such that the leverarm offset between each satellite’s antenna phase center andits center of gravity is properly considered. To do this, GNSSsatellite type dependent known lever arm offsets and attitudemodels [24, 25] must be included in the processing strategy.
In this study, we assume access to dual-frequency GNSSdata. As such, we use the dispersive nature of the ionosphere’sdelay and form a linear combination of the dual-frequencysignals in order to cancel the effect of the ionospheresignal refraction to the first order. This linear combinationis denoted as ionospheric-free (IF) combination [22] andgiven by (4) and (5), for pseudorange and carrier-phaseobservations, respectively:
𝜌
𝑗
IF = 𝜌
𝑗
𝐿1 [𝑓
21
𝑓
21 − 𝑓
22
] − 𝜌
𝑗
𝐿2 [𝑓
22
𝑓
21 − 𝑓
22
] , (4)
𝜙
𝑗
IF = 𝜙
𝑗
𝐿1 [𝑓
21
𝑓
21 − 𝑓
22
] − 𝜙
𝑗
𝐿2 [𝑓
22
𝑓
21 − 𝑓
22
] . (5)
Note that the coefficients in (4) and (5) (i.e., 2.546 and −1.546for GPS) sum to 1.0, and thus the modeled common modeerror sources, including clock biases and the tropospheredelay, remain unchanged in the IF observations. However,when using the IF combination, the unmodeled randomerrors denoted by 𝜖 become amplified. ForGNSS, the unmod-eled error sources consist of thermal noise and receiver frontend noise and multipath. For pseudorange observables 𝜖𝜌 ison the order of 1meter and for carrier-phase 𝜖𝜙 is on the orderof 1 millimeter. As such, when using the IF combination,the measurement noise is ∼3 meters for pseudorange and 3millimeters for carrier-phase (i.e., 3 ≈
√2.546
2+ 1.546
2).In (1) and (2), the tropospheric delay 𝑇
𝑗
𝑖 is typicallymodeled by scaling the zenith direction delay using anelevation angle dependent mapping function to reduce thenumber of model parameters. Furthermore, this is composedof both wet and dry components of which the dry componentis∼90%of the total delay and can bewell approximatedwith amodel. As such, the zenith dry delay is typically modeled andthe zenith wet delay is estimated as an unknown parametersuch that the delay is modeled as shown in
𝑇
𝑗
𝑖 = 𝑇𝑧Dry𝑀Dry
(el𝑗𝑖 ) + 𝑇𝑧Wet𝑀Wet(el𝑗𝑖 ) , (6)
where el𝑗𝑖 is the elevation angle from the nominal userlocation to satellite 𝑗. Within this study, different mappingfunctions, 𝑀Dry
,𝑀
Wet, are utilized depending on the solu-tion strategy and software used as will be detailed in the nextsection.
The remaining modeled error sources are the carrier-phase ambiguities. Traditionally, with kinematic PPP tech-niques, despite the fact that these are known to be an integernumber, these are modeled as floating point parameters inthe PPP filter/smoother. However, PPP ambiguity resolutiontechniques have been developed [26, 27] and this remains anactive research area.
An important unmodeled error source within the 𝜖 termsis present in (1) and (2) which are the errors induced by mul-tipath reflections. These errors are attributed to reflectionsof the GNSS signals being present in the received signal inaddition to the line of sight signal. Unfortunately, multipathleads to errors that are non-Gaussian and non-White innature, such that Kalman or least-squares type estimatorsare not best suited to mitigate them. Instead, a total least-squares processing technique could be employed, such asthe one mentioned in Juang [28]. However, the multipathinduced errors for carrier-phase are multiple orders of mag-nitude smaller than those for pseudorange. Further, for manyairborne applications, multipath induced errors, due to signalreflections from man-made objects, are less of a potentialproblem. In this study, to mitigate multipath induced errors,our PPP estimators will heavily rely on carrier-phase datarelative to pseudorange data.
2.2. Kinematic PPP with JPL’s GIPSY-OASIS. The first PPPapproach considered in this study uses Caltech JPL’s GNSS-Inferred Positioning System and Orbit Analysis Simula-tion Software (GIPSY-OASIS) 6.2 [29]. GIPSY has beenthe primary geodetic and positioning software for NASA’sTOPEX/Poseidon [30] and JASON [31] and GRACE [32] lowEarth orbiting spacecraft and is operationally used to generateJPL’s precise GPS orbits and clock products for the IGS [33].GIPSY is licensed for free by Caltech to institutions for use inacademic research.
When using GIPSY for kinematic PPP, our strategy inthis study is to iteratively process the position solution whilevaryingGIPSY configuration parameters in order to convergeit to an optimal solution that is free of data outliers. A blockdiagramof the processing strategy is shown in Figure 1, whichrequires defining some GIPSY terms.
(i) GNSS Data to Positioning (GD2P). It is GIPSY’s main userinterface script for PPP.
(ii) Pseudorange Data to Positioning (PR2P). It is GIPSY’sscript for pseudorange-only point positioning.
(iii) Time Dependent Parameter (TDP). It is GIPSY’s outputformat for positioning solutions and other solved for param-eters (e.g., clock biases, troposphere, and phase biases).
(iv) QM File. It is GIPSY’s native binary GNSS measurementformat.
As indicated in Figure 1, for the first iteration, a positionsolution is estimated using only pseudorange measurementwithGIPSY’s PR2P. In addition, the data is translated from theReceiver Independent Exchange Format (RINEX) to a GIPSY
4 International Journal of Aerospace Engineering
Inputs
Optional
Number of iterationsData weights
Postfit windowsMinimum slip
Stochastic properties
Preprocessing
GenerateQM file
PR2P
QM fileInitial TDP file
Required
RINEX fileData rate
Day
Defined inputs
Processing
GD2P
Iterate overQM file using
updated TDP filewith respect todefined inputs
FilterTDP file
Figure 1: Kinematic PPP strategy with GIPSY-OASIS. A wrapper software is used to interactively process the position solution.
binary QM file. During this process, a GNSS data editoris used to flag carrier-phase breaks and remove gross dataoutliers [34]. For data editing, the GIPSY defaults were usedwith the exception of the editor requiring aminimumdata arclength for a given transmitter. This is due to the short overallobservation window of the flights.
For the remaining iterations, a subset of GIPSY process-ing options are varied while accepting the previous positionsolution (TDP file) as the a priori position solution. WithinFigure 1, the configuration options that are varied for eachrun are as follows.
(i) Data Weights.They are measurement noise ratio betweenpseudorange and carrier-phase measurements. This starts asone-to-one and varies to one-hundred-to-one, where carrier-phase data are modeled as 100 times more precise thanpseudorange data.
(ii) Postfit Residual Window. Within each GIPSY processingrun, multiple passes of a Kalman filter and smoother areconducted. Between each pass, postfit data residuals are
evaluated and data are marked as outlier based on definedthresholds and excluded from the next pass. At each pass,the residuals of all data, inlier and outlier, are evaluated andeither added back in or excluded from the run. This processis repeated until all data meet the postfit window criteria or amaximum number of iterations are exceeded.
(iii) Stochastic Models. The position and wet tropospheredelay estimates can be modeled using either white noiseabout the nominal solution or random walk process noise.Additionally, the a priori 𝜎 magnitude and rate of processnoise updates can be set. In particular, the wet zenith delaywas estimated as a randomwalk process, given that the SUAVevaluated is not flying over great distances. Position is initiallyestimated using random walk, and after a few iterations itis estimated using white noise about an a priori nominalsolution.
(iv) Minimum Slip. After each filter iteration, jumps in thepostfit phase residuals are used to identify the possibility of
International Journal of Aerospace Engineering 5
Table 1: GIPSY wrapper options of kinematic PPP of SUAV data. Using the process shown in Figure 1.
a carrier-phase break that was missed by the data editor. Newbreaks are flagged for the next iteration.
In addition to the configuration parameters listed abovethat are varied for each iteration, several other GIPSY optionswere selected and held fixed in this study. In particular, thetroposphere mapping function used is the Niell mappingfunction [35] and the nominal troposphere delays were setusing the atmospheric model populated with a nominalheight for scaling and pressure and temperature from theGlobal Pressure and Temperature model [36]. For the severalremaining availableGD2Poptions (e.g., elevation cut-off, tidemodels), the defaults provided by JPL were used.
The specific strategy used for this study with respect toFigure 1 is listed in Table 1, for the 10 iterations conducted.
While the outlier deletion windows are selected ad hocbased upon experience, in order to assess the effectiveness ofpostfit data residual analysis and outlier deletion, the GIPSYlog files report an approximate 𝜒
2 statistic of the residualsfor each filter/smoother and data editing iteration. The valuereported is only approximate, because it is reported as ifthe entire data set were processed as least-squares batch asopposed to a sequential filter. More formally, the ResidualStandard Error (RSE) of the estimator for each outlier editingiteration is reported as follows:
𝜎RSE =√
RSOS𝑁 − 𝐷
,(7)
where RSOS is the Residual Sum of Squares normalizedto the data weight of each type of observation, 𝑁 is thetotal number of GNSS observations, and 𝐷 is the totalnumber of parameters estimated. In addition, while it mayseem problematic to delete data based upon user selectedthresholds, in practice only gross outliers are removed fromthe filter run.This is because the residual analysis is done in asequential narrowing window manner, such that such that,first, only gross outliers are deleted and then the residualsare reevaluated, with the possibility of adding data that wasflagged as outlier on a previous run as being marked as inlieragain (e.g., to handle the case in which one large outlierpollutes all of the residuals for a given epoch). Figure 2 showsan example for the RSE as well as the total percentage ofdata deleted during a GIPSY run, where the RSE is shownto converge and less than 1.5% of data is shown to have beendeleted.
2.3. Kinematic PPP with RTKLIB. The second software pack-age used for PPP in this study is the open-source RTKLIB[37, 38]. When using RTKLIB, several processing options areavailable for the user.The following list describes the adoptedprocessing strategy of this study.
(i) Kalman Filter Set-Up. The Kalman estimator was config-ured for both forward filtering and then backwards smooth-ing.
(ii) Elevation Cut-Off. A 5∘ elevation angle cut-off was used.
(iii) Troposphere Model.The troposphere was modeled usingthe Saastamoinen model and a residual wet zenith delay wasestimated.
(iv) Ionosphere. The ionosphere free linear combination wasused.
(v) Misc. Solid Earth tides and ocean loading tides weremodeled. Phase windup was considered.
(vi) Process Noise.The SUAV dynamics were modeled using adouble integrator with process noise driving the accelerationstates of 10 m/s2.
These options were selected using RTKLIB’s graphicaluser interface.
2.4. Carrier-PhaseDouble-Differenced Processing for ReferenceSolutions. To provide reference position solutions for thekinematic PPP solutions, a carrier-phase double-differencedinteger ambiguity fixed processing strategy was used. In thiscase, the GNSS error sources present in (2), in commonwith a GNSS base station, which is located at a well-knownlocation within a short baseline separation, are canceled viadata differencing [22]. In this scenario, the relative positionof the UAV with respect to the base station, 𝑟𝑈,𝐵, is estimated,and the known location of the base station is added to recoveran absolute position estimate of the UAV. For this technique,first, two carrier-phasemeasurements from the same satellite,𝑗, are differenced between the two user receivers, denotedhere as 𝑈, for UAV, and 𝐵, for base station, to form single-differenced carrier-phase measurements:
Δ𝜙
𝑗
𝑈,𝐵 = 𝜆
−1𝑟
𝑗
𝑈,𝐵 +𝑐
𝜆
𝛿𝑡𝑖𝑈,𝐵 + 𝑁
𝑗
𝑈,𝐵 + 𝜖
𝑗
𝜙,𝑈,𝐵, (8)
6 International Journal of Aerospace Engineering
Iterations number
% of deleted dataResidual Standard Error (RSE)
2 4 6 8 10 12 14
0
2
4
6
8
10
N=
72
,806
obse
rvat
ions
, RSE
[—]
Figure 2: Example of GIPSY’s iterative outlier deletion strategy.
where the satellite clock bias errors, the troposphere delay,and ionosphere delay are eliminated, and the ambiguity𝑁
𝑗
𝑈,𝐵 remains an integer. Next, to further eliminate theerror attributed to the combined users’ receiver clock biases,𝛿𝑡𝑈,𝐵, two of the single-differenced carrier-phase measure-ments from satellites 𝑗 and 𝑘 are subtracted to formdouble-differenced carrier-phase measurements, ∇Δ𝜙
𝑗,𝑘
𝑈,𝐵.The double-differencing process requires the selection of areference satellite which is typically selected to be a high-elevation satellite (indicated herein with index 𝑘) and sub-tracting its single-differenced measurement from all otheravailable single-differenced measurements. With double-differenced measurements, the only errors that remain arethe multipath errors, which are small for carrier-phaseobservables and airborne applications, and the ambiguity,which is known to be an integer number of wavelengths ofthe carrier frequency.
To resolve the integer ambiguity, a Kalman filter firstestimates the carrier-phase ambiguities as floating pointparameters, and, then, a separate technique is used to totake advantage of the fact that these states are an integernumber of wavelengths. In particular, the de facto techniquethat is used in this study is known as the Least-squares AMBi-guity Decorrelation and Adjustment (LAMBDA) method[39, 40]. The objective of the LAMBDA method is to findan Integer Least Squared Solution (ILS) with respect tothe estimated float ambiguities,
𝑁𝜙, and a correspondingvariance-covariance estimate of the phase ambiguities,𝑃��𝜙 ,��𝜙[39]. This is done by finding an orthogonal transformationthat preservers integer values and decorrelates 𝑃��𝜙,��𝜙
toa diagonal covariance matrix, such that simple roundingcan be employed to estimate the integer states. Followingthe rounding process, the transformation is reversed to getback into the state-space domain. The cost function that theLAMBDAmethod optimizes is given by [41]
𝐹 (𝑁𝜙) = (
𝑁𝜙 − 𝑁𝜙)𝑇𝑃
−1
��𝜙 ,��𝜙(
𝑁𝜙 − 𝑁𝜙) ≤ 𝜒
2,
𝑁𝜙 ∈𝑍
𝑛,
(9)
Figure 3: Phastball SUAV research platform. The two GNSSantennas are separated by an 85.3 cm baseline.
where the integer grid search space is defined by 𝜒
2. Oncethe integer fixed biases have been determined, the relativenavigation states are adjusted by assuming that the integer-fixing process is deterministic, such that the nonambiguitystates are corrected as
𝑥
fixposition = 𝑥
floatposition − 𝑃position,��𝜙𝑃��𝜙,��𝜙 (
𝑁𝜙 − 𝑁𝜙) , (10)
where 𝑃 refers to the variance-covariance matrix for thefloating point ambiguities that were estimated by the Kalmanfilter, of which particular sections are identified by thesubscripts position, which refers to the position states, and
𝑁𝜙, which refers to phase ambiguity states.It is important to point out that integer bias fixing will
not always be a success in the presence of errors. As such,there must be a validation process. The specific acceptance-test employed in the RTKLIB implementation used in thisstudy was the ratio-test [42]. The ratio-test evaluates howclose the float ambiguity estimates are to the best integerambiguity estimates when compared to the next best integerambiguity candidate.The best candidate,𝑁1st𝜙 , and the secondbest candidate, 𝑁2nd𝜙 , are defined as those that minimize thecost function 𝐹(𝑁𝜙) of (9):
Accept𝑁1st𝜙 iff𝐹 (𝑁
1st𝜙 )
𝐹 (𝑁
2nd𝜙
)
≤
1
𝐶
, (11)
where 𝐶 is the critical value, which can be derived on thefly to allow a fixed failure rate or set to a constant [42]. Forthis study, 𝐶 was set to 3 and held constant. Three is oftenused in practice, though this is only empirically justified [42].Throughout this study, only the epochs that were successfullyfixed and passed the ratio-test criterion, which ranged from65 to 85% of all epochs of each flight, were used as thereference solution for conducting the error analysis presentedbelow.
3. Experimental Set-Up
The Phastball SUAV airframe [43] was developed as a modu-lar research platform and has been used for multiple sensor-fusion studies [44–46].The Phastball Zero SUAV is shown inFigure 3.
International Journal of Aerospace Engineering 7
OEM-615 Novatel
4 ADIS16405 IMUs
A/D
PPS
Netburner MOD-5213
DataOpenLogSD logger
OpenLogSD logger
Pitch/rollvertical gyro
Pilot input channels
Base station/OEM-615
Novatel
900 Mhzmodem
OEM-615 Novatel
Figure 4: Phastball SUAV data acquisition set-up. Two GNSS receivers are logged in addition to IMU, mechanical vertical gyroscope, andground pilot input data.
For this study, its payload features two Novatel OEM-615 dual-frequency GNSS receivers with antennas separated85.3 cm along the airframe’s longitudinal axis. A block dia-gram of Phastball Zero’s data acquisition structure is shownin Figure 4.
In this set-up, oneNovatel Receiver isGPS andGLONASScapable and the other is GPS only. RawGNSS dual-frequencypseudorange and carrier-phase observables are recorded ata rate of 10Hz using OpenLog serial microSD data-loggers.The GPS/GLONASS Novatel OEM-615 receiver is wirelesslyconnected through a 900MHz modem to a base station thatsends up RTKdifferential correctors. Additionally, amechan-ical vertical gyroscope that directly measures the UAV’s pitchand roll is included onboard, as well as the pilot input andfour Analog Devices ADIS-16405 MicroelectromechanicalSystems (MEMS) IMUs, which are interfaced through twoNetburner MOD-5213 microcontrollers logging data withOpenLog serial stream data-loggers. For postprocessing, therecorded GNSS data and data streams that are interfacedthrough the Netburner MOD-5213 microcontroller are syn-chronized by recording the state of the Pulse-Per-Second(PPS) signal from one of the GNSS receivers.
In addition to the Phastball SUAV, the experimental set-up consisted of another Novatel OEM-615 dual-frequencyreceiver serving as a static reference receiver with the antennamounted on a tripod. Experimental flight-tests for this studywere conducted at WVU’s Jackson’s Mill airfield. A typicalflight pattern is shown in Figure 5.
In total, six data sets of short duration SUAV flights werecollected for this study. These consisted of three flight-testswith two data sets per flight. Table 2 lists the total flightduration from take-off to landing of the three flights.
Figure 5: Birdseye view of typical Phastball SUAVflight at theWVUJackson’s Mill airfield. Image was generated using Google Earth.
Table 2: SUAV flight test durations.
Flight # Duration (s)1 156.22 342.43 264.0
4. Results and Discussion
4.1. Validation of Reference Position Solutions. For com-paring the estimation performances of various PPP andsingle receiver point positioning algorithms, Kalman fil-ter/smoother CP-DGPS solutions were generated for each
8 International Journal of Aerospace Engineering
Difference between RTK GPS solutionsMeasured with a tape measureMean RTK difference
1 2 3 4 50
Time into flight (min)
0.84
0.845
0.85
0.855
0.86
0.865
0.87
Ant
enna
sepa
ratio
n (m
)
Figure 6: Phastball Zero SUAV GNSS antenna baseline separationas estimated by differencing the two RTK GPS solutions that arebeing used as reference solutions for PPP comparisons and bymeasuring with a tape measure.
flight-test with respect to a local GPS reference station set-upat the airfield. When processing the CP-DGPS data, in orderto obtain the absolute coordinates of the base station’s tripod,∼6 hours of static data was processing using GIPSY-OASISPPP in static mode.The software that was used for generatingthe CP-DGPS reference solutions was RTKLIB 2.4.2.
While it is well known that double-difference integerfixed CP-DGPS solutions can obtain cm-level accuracy andprecision, the Phastball flight-test configuration provides theopportunity to validate this level of accuracy and precision forthe reference position solutions. In particular, the PhastballSUAV is outfitted with two GPS antennas separated by aknown baseline distance of 83.5 cm. Note that, with thisset-up, it is possible to further leverage the known baselineconstraint between the multiple antennas to improve esti-mation performance of position and attitude [47], whichcan further be extended to improvements with an array ofmultiple antennas (i.e.,more than 2) [48, 49].While the array-aided PPP is an interesting research direction that the authorsintend to pursue with this SUAV platform, for the presentstudy, the goal is to assess the accuracy of single antennaPPP for SUAVs. Therefore, in order to validate the referencesolutions used for each separate antenna, the two ambiguityfixed CP-DGPS solutions for each receiver on the SUAVweredifferenced, and the magnitude of the difference was used toevaluate how well the known antenna separation distance isestimated. Figure 5 shows an example of the result of thisanalysis for our second SUAV flight-test.
As shown in Figure 6, the separation between the twoantennas was estimated with both cm-level accuracy andprecision. Table 3 shows the antenna separation estimationerror for all three flights, where sub-cm accuracy and cm-level precision were obtained.
Table 3: 85.3 cm antenna baseline estimation performance using theRTK reference solutions for the three SUAV flight tests considered.
4.2. Performance Comparison Study. In order to provide acontext, in addition to the PPP solution methods describedin Section 2, position solutions obtained by processing thepseudorange data only with the GPS broadcast ephemerisusing both the GIPSY software and the RTKLIB softwareare presented. These solutions represent the expected levelof accuracy one would obtain from a GPS receiver positionsolution without any DGPS or PPP products. Short nameidentifiers for the processing strategies that were comparedare shown in Table 4.
Table 5 shows the mean and standard deviation errorstatistics for the four processingmethods considered over thesix data sets, and Table 6 shows the overall average meanerror and standard deviation error over the six flights, whereall solutions are compared to the ambiguity fixed CP-DGPSreference solutions.
As shown in Tables 5 and 6, when using pseudorangebased point positioning, 2-3 meters-level precision and accu-racy can be expected. However, when adopting kinematicPPP, decimeter-level accuracy and centimeter-level precisionwere obtained, despite the fact that these are flight data setswith only a few minutes of observations. Further, to obtainthis level of positioning performance, all the user needs to dois collect the raw GNSS measurements for postprocessing.
While the level of precision on short duration SUAVflights is centimeter-level, decimeter-level biases remain inthe solution. It is expected that these are likely due to the shortduration data set and the known slow convergence of PPP.However, an important insight provided by this study is thatwhen considering short duration postprocessing applicationsof PPP, the slow convergence yields a constant bias, that is,when considering the error sources that must be modeledor mitigated by PPP in (1) and (2) (e.g., troposphere, orbit,clock, and phase ambiguities). Despite the fact that thereis no enough data to converge upon the absolute values ofthese error sources, each of these error sources remains quiteconstant over the few minutes’ time-scale. Therefore, thesedecimeter-level biases can easily be mitigated by starting theSUAVat a known location (e.g., by placing a receiver at a take-off location for static PPP) or simply allowing the SUAV to sitstatic on the runway for an initialization period.
To further substantiate why kinematic PPP with shortobservational periods is still very precise but biased, anadditional five-minute SUAV flight that was simulated usinga PPP simulation tool developed for a previous study [16]was analyzed. With this tool, all of the GNSS error sourcesdiscussed in Section 2.1 are modeled, but because theyare simulated, perfect knowledge about all error sourcesis available for analysis. As such, the performance withrespect to a perfectly known truth was assessed. Figure 7
International Journal of Aerospace Engineering 9
Table 4: Short names and definitions for the PPP solution strategies evaluated.
Short name Solution strategy descriptionPR2P-PP Dual-frequency pseudorange measurement-only point positioning using broadcast ephemerisRTKLIB-PP Single receiver point positioning using RTKLIB with broadcast ephemerisGD2P-PPP Kinematic PPP using JPL final GPS orbit and clock products and the processing method described in Section 2.2
RTKLIB-PPP Kinematic PPP using International GNSS Service combined final GPS orbit and clock products and methoddescribed in Section 2.3
Table 5: Mean and standard deviation positioning error statistics by positioning approach for each flight.
Receiver Flight 1 Flight 2 Flight 3Front Back Front Back Front Back
shows an example kinematic PPP forward filter’s positionsolution errors and phase bias estimation errors, as well asthe backwards Rauch-Tung-Striebel [50] Kalman smoothedposition and phase bias errors.
As shown in Figure 7, a similar level of positioningperformance as presented in the flight data analysis is shownfor the simulated flight, that is, decimeter-level accuracy
with centimeter-level precision. Further, the phase biases,which are estimated as random constants, do convergebut maintain approximately 10 to 15 cm biases after the 5minutes. Then, during the backwards smoother, the phasebias estimates are nearly constant, leading to considerablysmoother positioning errors, as shown, but with decimeter-level biases remaining present. In particular, the mean errorsbetween the forward filter and smoother are only reduced by1% from 44 cm to 45 cm; however, the standard deviation ofthe position errors was reduced by more than 25% with a 3D𝜎 reduction from 14.7 cm to 11 cm.
5. Conclusions
An experimental evaluation of kinematic PPP using shortduration SUAV data has been presented, as such a studywas missing in the literature and the PPP approach hasyet to be heavily leveraged in the field robotics and SUAVcommunities.Through comparison with CP-DGPS reference
10 International Journal of Aerospace Engineering
solutions, it has been shown that approximately 6 cm3Dposi-tioning precision with decimeter-to-meter-level 3D accuracyis obtainable when using PPP even when the flights are onlya few minutes in duration. This is of benefit because PPPdoes not require the user to have access to a differentialreference station. This result has been demonstrated withsix SUAV flight data sets and two popular GNSS processingsoftware packages. The results of this study are of benefitto many potential SUAV science applications that requireprecise positioning.
Competing Interests
The authors declare no conflict of interests with the publica-tion of this paper.
Acknowledgments
This research was partially supported by the US NationalGeospatial Intelligence Agency Academic Research Program(NARP) Grant no. HM0476-15-1-0004. Approved for publicrelease, case no. 16-195.
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